Many-Body Methods in Nuclear Structure and Related Fields

本提案的中心主题是发展近似求解原子核薛定谔方程的新方法，并将其应用于当代核结构物理中的重要问题。在核壳模型和平均场理论中有其根源的方法将被考虑，以开发显着扩展其适用范围的算法为目标。主要的焦点将放在密度矩阵重整化群（DMRG）的发展上，这是一种在量子自旋晶格背景下首次引入的方法。在这里，我们将重点讨论一种新的DMRG方法，这种方法是为原子核这样的有限费米系统量身定制的。我们还将考虑它在一个重要的非核问题上的应用，二维哈伯德模型，它与在高温临界温度下过渡到超导的系统有关。第二个重点将放在远离稳定的弱束缚原子核的性质上。最近提出的一种可靠地求解非常弱束缚原子核的Hartree Fock Bogolyubov平均场方程的方法将进一步发展，使其在计算上更可行，然后将系统地应用于整个元素周期表的球形和轴向变形原子核。在弱界系统中求解Hartree Fock Bogolyubov方程的其他方法也将被考虑，以确保这种系统的空间性质被可靠地处理。

The central theme of this proposal is the development of new methods for approximately solving the Schroedingerequation for atomic nuclei and their application to problems ofcontemporary importance in nuclear structure physics. Methods having their parentage in the nuclear shell model and in mean-field theory will be considered, with the goal of developing algorithms that significantly expand their ranges of applicability. A principal focus will be on the development of theDensity Matrix Renormalization Group (DMRG), a method first introduced in the context of quantum spin lattices. Here we will focus on a new DMRG methodology that is tailored to such finite fermi systems as the atomic nucleus. We will also consider its application to an important non-nuclear problem, the two-dimensional Hubbard model, which is of relevance to systems that undergo transitions to superconductivity at high critical temperatures. A second focus will be on the properties ofweakly-bound nuclei far from stability. A method recently proposed for reliably solving the Hartree Fock Bogolyubov mean-field equations for very weakly-bound nuclei will be developed further, so as to make it computationally more viable, and will then be applied systematically to both spherical and axially-deformed nuclei throughout the periodic table. Other methods for solving the Hartree Fock Bogolyubov equations in weakly-bound systems will also be considered, to make sure that the spatial properties of such systems are being reliably treated.